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In summary, the gradient of a function is a vector that gives the rate of change of the function in a given direction. It is perpendicular to the level curves of the function and the direction of steepest ascent. This can be visualized by imagining walking along a level path on a hill, where the steepest slope is perpendicular to the path. The concept of steepest descent and conjugate gradient methods can be further understood through resources like the article from Better Explained and videos from Khan Academy.

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https://betterexplained.com/articles/vector-calculus-understanding-the-gradient/

Khan Academy has some videos too:

https://www.khanacademy.org/math/mu...-gradient-is-the-direction-of-steepest-ascent

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https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf

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